Is Space-Time Non-Commutative? Understanding Non-Commutative Geometry in Physics

[black hole 123]

ive been reading about people thinking sub Planck scale spacetime is "non commutative". i have a vague idea of non commutative geometry mathematically, but there's no "space" in non commutative geometry so how can SPACEtime be a non commutative ring?

i thought non commutative geometry was just a mathematical generalization of normal (commutative) algebraic geometry. I am not a physics students so I am not in a position to judge, but i find many things in math applied to physics with absolutely NO physical manifestation/interpretation

sorry if this sounds stupid

 

[ohwilleke]

Non-commutative geometry, in a nutshell, means that distance is a path dependent quantity and that for example, the distance from X to Y via a path, and the trip back may have different distances.

A non-fundamental example would be the geography of getting from one place to another in a city with lots of one way streets and irregular loops (e.g. Boston). The distance from your house to your office may be different from the distance from your office to your house.

Obviously, when this is operating at a fundamental level as a basic element of the structure of space-time, getting your head around the idea is much harder. But, this is the idea at its most basis level.